
import pandas as pd
import numpy as np
import seaborn as sns
import plotly.express as px
import plotly.graph_objects as go
import plotly.figure_factory as ff
import matplotlib.pyplot as plt
%matplotlib inline
import prince as ps
from sklearn.decomposition import PCA
from sklearn.preprocessing import scale
import dtale
from autoviz.AutoViz_Class import AutoViz_Class
AV = AutoViz_Class()
import scipy.cluster.hierarchy as sch
from sklearn.cluster import AgglomerativeClustering
from yellowbrick.cluster import KElbowVisualizer
from yellowbrick.cluster import SilhouetteVisualizer
from scipy.cluster.hierarchy import dendrogram, linkage
from sklearn.metrics import silhouette_score
from sklearn.cluster import KMeans
from mpl_toolkits import mplot3d
from scipy.spatial.distance import cdist
from sklearn.manifold import TSNE
from bioinfokit.visuz import cluster
from sklearn.feature_extraction.text import TfidfVectorizer
from yellowbrick.text import TSNEVisualizer

Imported AutoViz_Class version: 0.0.81. Call using:
    from autoviz.AutoViz_Class import AutoViz_Class
    AV = AutoViz_Class()
    AV.AutoViz(filename, sep=',', depVar='', dfte=None, header=0, verbose=0,
                            lowess=False,chart_format='svg',max_rows_analyzed=150000,max_cols_analyzed=30)
Note: verbose=0 or 1 generates charts and displays them in your local Jupyter notebook.
      verbose=2 saves plots in your local machine under AutoViz_Plots directory and does not display charts.


df= pd.read_csv("E:\ExcelR Assignment\Assignment 8 - PCA\wine.csv")
df.head()


df.isnull().sum()

Type               0
Alcohol            0
Malic              0
Ash                0
Alcalinity         0
Magnesium          0
Phenols            0
Flavanoids         0
Nonflavanoids      0
Proanthocyanins    0
Color              0
Hue                0
Dilution           0
Proline            0
dtype: int64


df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 178 entries, 0 to 177
Data columns (total 14 columns):
 #   Column           Non-Null Count  Dtype  
---  ------           --------------  -----  
 0   Type             178 non-null    int64  
 1   Alcohol          178 non-null    float64
 2   Malic            178 non-null    float64
 3   Ash              178 non-null    float64
 4   Alcalinity       178 non-null    float64
 5   Magnesium        178 non-null    int64  
 6   Phenols          178 non-null    float64
 7   Flavanoids       178 non-null    float64
 8   Nonflavanoids    178 non-null    float64
 9   Proanthocyanins  178 non-null    float64
 10  Color            178 non-null    float64
 11  Hue              178 non-null    float64
 12  Dilution         178 non-null    float64
 13  Proline          178 non-null    int64  
dtypes: float64(11), int64(3)
memory usage: 19.6 KB


df.describe()


df['Type'].value_counts()

2    71
1    59
3    48
Name: Type, dtype: int64


fig = px.pie(df['Type'], values='Type', names='Type',color_discrete_sequence=px.colors.sequential.Blackbody)
fig.show()


sns.distplot(df)

<AxesSubplot:ylabel='Density'>


dtale.show(df, ignore_duplicate=True)


df = AV.AutoViz("E:\ExcelR Assignment\Assignment 8 - PCA\wine.csv")

Shape of your Data Set: (178, 14)
############## C L A S S I F Y I N G  V A R I A B L E S  ####################
Classifying variables in data set...
    Number of Numeric Columns =  11
    Number of Integer-Categorical Columns =  3
    Number of String-Categorical Columns =  0
    Number of Factor-Categorical Columns =  0
    Number of String-Boolean Columns =  0
    Number of Numeric-Boolean Columns =  0
    Number of Discrete String Columns =  0
    Number of NLP String Columns =  0
    Number of Date Time Columns =  0
    Number of ID Columns =  0
    Number of Columns to Delete =  0
    14 Predictors classified...
        This does not include the Target column(s)
        No variables removed since no ID or low-information variables found in data set
Number of All Scatter Plots = 66

Time to run AutoViz (in seconds) = 135.542

 ###################### VISUALIZATION Completed ########################


fig = px.imshow(df.corr())
fig.show()


fdf = df.drop(['Type'],axis=1)


fdf.head()


def stand_func(i):
    x = (i-i.mean())/(i.std())
    return (x)


sdf = stand_func(fdf)


sdf.head()


sns.distplot(sdf)

<AxesSubplot:ylabel='Density'>


pca = PCA(random_state=42)
pca_values = pca.fit_transform(sdf)


cum_nvariance = np.cumsum(pca.explained_variance_ratio_*100)
cum_nvariance

array([ 36.1988481 ,  55.40633836,  66.52996889,  73.59899908,
        80.16229276,  85.09811607,  89.3367954 ,  92.01754435,
        94.23969775,  96.16971684,  97.90655253,  99.20478511,
       100.        ])


# Variance plot for PCA components obtained 
plt.plot(cum_nvariance,color="red")
plt.xlabel('Number of PCA components')
plt.ylabel('Cumulative Variance')
plt.axhline(y=95, color='k', linestyle='--')
plt.text(0.1, 97, '95% cut-off threshold', color = 'red', fontsize=10)
plt.title('PCA Components vs Variance Plot')

Text(0.5, 1.0, 'PCA Components vs Variance Plot')


a=pca_values[:,0:1]
b=pca_values[:,1:2]
d=pca_values[:,2:3]


fig = plt.figure(figsize = (16, 9))
ax = plt.axes(projection ="3d")

ax.grid(b = True, color ='grey',
        linestyle ='-.', linewidth = 0.3,
        alpha = 0.2)

my_cmap = plt.get_cmap('hsv')

sctt = ax.scatter3D(a, b, d,
                    alpha = 0.8,
                    c = (a + b + d),
                    cmap = my_cmap,
                    marker ='^')

plt.title("simple 3D scatter plot")
ax.set_xlabel('PCA-1', fontweight ='bold')
ax.set_ylabel('PCA-2', fontweight ='bold')
ax.set_zlabel('PCA-3', fontweight ='bold')
fig.colorbar(sctt, ax = ax, shrink = 0.5, aspect = 5)

plt.show()


pcastd = pd.DataFrame(pca_values,columns=['pca1','pca2','pca3','pca4','pca5','pca6','pca7','pca8','pca9','pca10','pca11','pca12','pca13'])
pcastd.head()


pcastd = pcastd.drop(['pca4','pca5','pca6','pca7','pca8','pca9','pca10','pca11','pca12','pca13'],axis=1)


pcastd.head()


for methods in ['single','complete','average','centroid']:
    z = linkage(pcastd,method=methods, metric = "euclidean")
    plt.figure(figsize=(20,6))
    plt.title('Hierarchical Clustering Dendogram, Method-{}'.format(methods))
    plt.xlabel('Index')
    plt.ylabel('Distance')
    sch.dendrogram(z)
    plt.show()


n_clusters = [2,3,4,5,6,7,8]  # always start number from 2.

for n_clusters in n_clusters:
    for linkages in ["single","complete","average","ward"]:
        hie_cluster = AgglomerativeClustering(n_clusters=n_clusters,linkage=linkages) # bydefault it takes linkage 'ward'
        hie_labels = hie_cluster.fit_predict(pcastd)
        silhouette_score1 = silhouette_score(pcastd, hie_labels)
        print("For n_clusters =", n_clusters,"The average silhouette_score with linkage-",linkages, ':',silhouette_score1)
    print()

For n_clusters = 2 The average silhouette_score with linkage- single : 0.36310673051041525
For n_clusters = 2 The average silhouette_score with linkage- complete : 0.3254686544245087
For n_clusters = 2 The average silhouette_score with linkage- average : 0.36310673051041525
For n_clusters = 2 The average silhouette_score with linkage- ward : 0.39509037225075366

For n_clusters = 3 The average silhouette_score with linkage- single : 0.2166287164412593
For n_clusters = 3 The average silhouette_score with linkage- complete : 0.28750089351606367
For n_clusters = 3 The average silhouette_score with linkage- average : 0.38672545200747754
For n_clusters = 3 The average silhouette_score with linkage- ward : 0.4459492198062964

For n_clusters = 4 The average silhouette_score with linkage- single : 0.1361608641214519
For n_clusters = 4 The average silhouette_score with linkage- complete : 0.3578484268567307
For n_clusters = 4 The average silhouette_score with linkage- average : 0.321731313111978
For n_clusters = 4 The average silhouette_score with linkage- ward : 0.3819569034814439

For n_clusters = 5 The average silhouette_score with linkage- single : 0.11138163769596811
For n_clusters = 5 The average silhouette_score with linkage- complete : 0.3558447987963538
For n_clusters = 5 The average silhouette_score with linkage- average : 0.4465449278023581
For n_clusters = 5 The average silhouette_score with linkage- ward : 0.3194881617466346

For n_clusters = 6 The average silhouette_score with linkage- single : 0.0048647373342952036
For n_clusters = 6 The average silhouette_score with linkage- complete : 0.3133623256988351
For n_clusters = 6 The average silhouette_score with linkage- average : 0.39074628143794893
For n_clusters = 6 The average silhouette_score with linkage- ward : 0.3199326987989737

For n_clusters = 7 The average silhouette_score with linkage- single : -0.10255716440985131
For n_clusters = 7 The average silhouette_score with linkage- complete : 0.24980278617073867
For n_clusters = 7 The average silhouette_score with linkage- average : 0.36330428689800437
For n_clusters = 7 The average silhouette_score with linkage- ward : 0.289022476357529

For n_clusters = 8 The average silhouette_score with linkage- single : -0.19366989657882092
For n_clusters = 8 The average silhouette_score with linkage- complete : 0.2675496836392119
For n_clusters = 8 The average silhouette_score with linkage- average : 0.2900448801576868
For n_clusters = 8 The average silhouette_score with linkage- ward : 0.26712344783971076


hc = AgglomerativeClustering(n_clusters=3, affinity = 'euclidean', linkage = 'ward')


y_hc = hc.fit_predict(pcastd)
Clusters=pd.DataFrame(y_hc,columns=['HClusters'])


Hdf = df.copy()
Hdf.head()


Hdf = pd.concat([Clusters,Hdf],axis=1)


Hdf.head()


plt.figure(figsize=(10,10))
Hdf.plot(x="HClusters",y="Type",c=y_hc,kind="scatter",s=50,cmap=plt.cm.gist_rainbow)
plt.title('Clustering using H-Clustering on Standardized Data')

Text(0.5, 1.0, 'Clustering using H-Clustering on Standardized Data')

<Figure size 720x720 with 0 Axes>


Hdf['HClusters'].value_counts()

0    66
2    65
1    47
Name: HClusters, dtype: int64


Hdf['Type'].value_counts()

2    71
1    59
3    48
Name: Type, dtype: int64


model = KMeans(random_state=42,max_iter=500,algorithm ='elkan')


visualizer = KElbowVisualizer(model, k=(2,15),metric='silhouette')


visualizer.fit(pcastd)
visualizer.poof()
plt.show()


k = list(range(2,10))
TWSS = [] # variable for storing total within sum of squares for each kmeans 
for i in k:
    kmeans = KMeans(n_clusters = i)
    kmeans.fit(pcastd)
    WSS = [] # variable for storing within sum of squares for each cluster 
    for j in range(i):
        WSS.append(sum(cdist(pcastd.iloc[kmeans.labels_==j,:],kmeans.cluster_centers_[j].reshape(1,pcastd.shape[1]),"euclidean")))
    TWSS.append(sum(WSS))


# Scree plot using code
plt.plot(k,TWSS, 'ro-');plt.xlabel("No_of_Clusters");plt.ylabel("total_within_SS");plt.xticks(k)

([<matplotlib.axis.XTick at 0x1bcc852c160>,
  <matplotlib.axis.XTick at 0x1bcc852c670>,
  <matplotlib.axis.XTick at 0x1bcc7e60580>,
  <matplotlib.axis.XTick at 0x1bcc9a612b0>,
  <matplotlib.axis.XTick at 0x1bcc9a61b20>,
  <matplotlib.axis.XTick at 0x1bcc9a61be0>,
  <matplotlib.axis.XTick at 0x1bcc9e68af0>,
  <matplotlib.axis.XTick at 0x1bcc9e68370>],
 [Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, ''),
  Text(0, 0, '')])


visualizer1 = SilhouetteVisualizer(model,k=(2,10),metric='distortion')
visualizer1.fit(pcastd)
visualizer1.poof()

<AxesSubplot:title={'center':'Silhouette Plot of KMeans Clustering for 178 Samples in 14 Centers'}, xlabel='silhouette coefficient values', ylabel='cluster label'>


list1= [2,3,4,5,6,7,8]  # always start number from 2.

for n_clusters in list1:
    clusterer1 = KMeans(n_clusters=n_clusters, random_state=42)
    cluster_labels1 = clusterer1.fit_predict(pcastd)
    sil_score1= silhouette_score(pcastd, cluster_labels1)
    print("For n_clusters =", n_clusters,"The average silhouette_score is :", sil_score1)

For n_clusters = 2 The average silhouette_score is : 0.38938813089003294
For n_clusters = 3 The average silhouette_score is : 0.4537999848257609
For n_clusters = 4 The average silhouette_score is : 0.4106780309460923
For n_clusters = 5 The average silhouette_score is : 0.3796688345419278
For n_clusters = 6 The average silhouette_score is : 0.30776741310572353
For n_clusters = 7 The average silhouette_score is : 0.3240137134136091
For n_clusters = 8 The average silhouette_score is : 0.29964389603190816


cl = KMeans(n_clusters = 3)
y_kmeans = cl.fit_predict(pcastd)
md=pd.Series(cl.labels_)  # converting numpy array into pandas series object 
Kdf = df.copy()
Kdf['KCluster']=md # creating a  new column and assigning it to new column 
Kdf.head()


Kdf['KCluster'].value_counts()

2    64
0    63
1    51
Name: KCluster, dtype: int64


Kdf['Type'].value_counts()

2    71
1    59
3    48
Name: Type, dtype: int64


plt.figure(figsize=(10,10))
Kdf.plot(x="KCluster",y="Type",c=cl.labels_,kind="scatter",s=50,cmap=plt.cm.gist_rainbow)
plt.title('Clustering using K-Clustering on Standardized Data')

Text(0.5, 1.0, 'Clustering using K-Clustering on Standardized Data')

<Figure size 720x720 with 0 Axes>


Hdf.to_csv("PCAHdfStd.csv")


Kdf.to_csv("PCAKdfStd.csv")


df.head()


array=df.values
X=array[:,1:]
Y=array[:,0]


data_tsne = TSNE(n_components = 3).fit_transform(X)
cluster.tsneplot(score=data_tsne)


x=data_tsne[:,0:1]
y=data_tsne[:,1:2]
z=data_tsne[:,2:3]


fig = plt.figure(figsize = (16, 9))
ax = plt.axes(projection ="3d")

ax.grid(b = True, color ='grey',
        linestyle ='-.', linewidth = 0.3,
        alpha = 0.2)

my_cmap = plt.get_cmap('hsv')

sctt = ax.scatter3D(x, y, z,
                    alpha = 0.8,
                    c = (x + y + z),
                    cmap = my_cmap,
                    marker ='^')

plt.title("simple 3D scatter plot")
ax.set_xlabel('tSNE-1', fontweight ='bold')
ax.set_ylabel('t-SNE-2', fontweight ='bold')
ax.set_zlabel('t-SNE-3', fontweight ='bold')
fig.colorbar(sctt, ax = ax, shrink = 0.5, aspect = 5)

plt.show()


color_class=Y
cluster.tsneplot(score=data_tsne,colorlist=color_class,legendanchor=(1.5,1))

	Type	Alcohol	Malic	Ash	Alcalinity	Magnesium	Phenols	Flavanoids	Nonflavanoids	Proanthocyanins	Color	Hue	Dilution	Proline
0	1	14.23	1.71	2.43	15.6	127	2.80	3.06	0.28	2.29	5.64	1.04	3.92	1065
1	1	13.20	1.78	2.14	11.2	100	2.65	2.76	0.26	1.28	4.38	1.05	3.40	1050
2	1	13.16	2.36	2.67	18.6	101	2.80	3.24	0.30	2.81	5.68	1.03	3.17	1185
3	1	14.37	1.95	2.50	16.8	113	3.85	3.49	0.24	2.18	7.80	0.86	3.45	1480
4	1	13.24	2.59	2.87	21.0	118	2.80	2.69	0.39	1.82	4.32	1.04	2.93	735

	Type	Alcohol	Malic	Ash	Alcalinity	Magnesium	Phenols	Flavanoids	Nonflavanoids	Proanthocyanins	Color	Hue	Dilution	Proline
count	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000	178.000000
mean	1.938202	13.000618	2.336348	2.366517	19.494944	99.741573	2.295112	2.029270	0.361854	1.590899	5.058090	0.957449	2.611685	746.893258
std	0.775035	0.811827	1.117146	0.274344	3.339564	14.282484	0.625851	0.998859	0.124453	0.572359	2.318286	0.228572	0.709990	314.907474
min	1.000000	11.030000	0.740000	1.360000	10.600000	70.000000	0.980000	0.340000	0.130000	0.410000	1.280000	0.480000	1.270000	278.000000
25%	1.000000	12.362500	1.602500	2.210000	17.200000	88.000000	1.742500	1.205000	0.270000	1.250000	3.220000	0.782500	1.937500	500.500000
50%	2.000000	13.050000	1.865000	2.360000	19.500000	98.000000	2.355000	2.135000	0.340000	1.555000	4.690000	0.965000	2.780000	673.500000
75%	3.000000	13.677500	3.082500	2.557500	21.500000	107.000000	2.800000	2.875000	0.437500	1.950000	6.200000	1.120000	3.170000	985.000000
max	3.000000	14.830000	5.800000	3.230000	30.000000	162.000000	3.880000	5.080000	0.660000	3.580000	13.000000	1.710000	4.000000	1680.000000

	Alcohol	Malic	Ash	Alcalinity	Magnesium	Phenols	Flavanoids	Nonflavanoids	Proanthocyanins	Color	Hue	Dilution	Proline
0	14.23	1.71	2.43	15.6	127	2.80	3.06	0.28	2.29	5.64	1.04	3.92	1065
1	13.20	1.78	2.14	11.2	100	2.65	2.76	0.26	1.28	4.38	1.05	3.40	1050
2	13.16	2.36	2.67	18.6	101	2.80	3.24	0.30	2.81	5.68	1.03	3.17	1185
3	14.37	1.95	2.50	16.8	113	3.85	3.49	0.24	2.18	7.80	0.86	3.45	1480
4	13.24	2.59	2.87	21.0	118	2.80	2.69	0.39	1.82	4.32	1.04	2.93	735

	Alcohol	Malic	Ash	Alcalinity	Magnesium	Phenols	Flavanoids	Nonflavanoids	Proanthocyanins	Color	Hue	Dilution	Proline
0	1.514341	-0.560668	0.231400	-1.166303	1.908522	0.806722	1.031908	-0.657708	1.221438	0.251009	0.361158	1.842721	1.010159
1	0.245597	-0.498009	-0.825667	-2.483841	0.018094	0.567048	0.731565	-0.818411	-0.543189	-0.292496	0.404908	1.110317	0.962526
2	0.196325	0.021172	1.106214	-0.267982	0.088110	0.806722	1.212114	-0.497005	2.129959	0.268263	0.317409	0.786369	1.391224
3	1.686791	-0.345835	0.486554	-0.806975	0.928300	2.484437	1.462399	-0.979113	1.029251	1.182732	-0.426341	1.180741	2.328007
4	0.294868	0.227053	1.835226	0.450674	1.278379	0.806722	0.661485	0.226158	0.400275	-0.318377	0.361158	0.448336	-0.037767

	pca1	pca2	pca3	pca4	pca5	pca6	pca7	pca8	pca9	pca10	pca11	pca12	pca13
0	3.307421	-1.439402	-0.165273	-0.215025	0.691093	-0.223250	0.594749	0.064956	0.639638	1.018084	-0.450293	0.539289	-0.066052
1	2.203250	0.332455	-2.020757	-0.290539	-0.256930	-0.924512	0.053624	1.021534	-0.307978	0.159252	-0.142256	0.387146	0.003626
2	2.509661	-1.028251	0.980054	0.722863	-0.250327	0.547731	0.423012	-0.343248	-1.174521	0.113042	-0.285866	0.000582	0.021655
3	3.746497	-2.748618	-0.175696	0.566386	-0.310964	0.114109	-0.382259	0.641783	0.052397	0.238739	0.757448	-0.241339	-0.368444
4	1.006070	-0.867384	2.020987	-0.408613	0.297618	-0.405376	0.442825	0.415528	0.325900	-0.078146	-0.524466	-0.216055	-0.079140

IMPORTING LIBRARIES¶

No Null values¶

Type is a Categorical Data, that can be used to create clusters¶

AUTO EDA¶

dtale Library for Auto Data Analysis¶

Autoviz Library for Auto Data Visualization¶

Inferences:¶

Transformation of variables¶

Applying Standardization¶

PCA¶

At around 8 PCA components we are getting 95% of data¶

1. H-Cluster¶

Silhouette_score = 0.45 with Cluster=3 is the better one amongst all¶

II. K-Means¶

Silhouette_score = 0.45 with Cluster = 3 is the better one amongst all¶

Saving to csv file¶

t-SNE Algorithm¶